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Nhân cả 2 vế với 2 ta có:
2P=24(52+1)(54+1)(58+1)(516+1)
2P=(52_1)(52+1)(54+1)(58+1)(516+1)
2P=(54_1)(54+1)(58+1)(516+1)
2P=(58_1)(58+1)(516+1)
2P=(516_1)(516+1)
2P=532_1
P=\(\frac{5^{32}-1}{2}\)
P = 12 ( 52 + 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=>2P=24 ( 52 + 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=( 52 - 1 ) ( 52 + 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=( 54 - 1 ) ( 54 + 1 ) ( 58 +1 ) ( 516 +1 )
=( 58 - 1 ) ( 58 +1 ) ( 516 +1 )
=( 516 - 1 ) ( 516 + 1 )
= 532 - 1
=>P=\(\frac{5^{32}-1}{2}\)
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(2P=5^{32}-1\)
\(P=\frac{5^{32}-1}{2}\)
P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=24(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=(5-1)(5+1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
2P=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
2P=(5^8-1)(5^8+1)(5^16+1)
2P=(5^16-1)(5^16+1)
2P=5^32-1
P=(5^32-1):2
\(P=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(P=\frac{1}{2}\left(5^{32}+1\right)\)
P=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
1/2P=24(5^2+1)(5^4+1)(5^8+1)(5^16+1)
1/2P=(5^2-1)(5^2+1)(5^4+1)(5^8+1)(5^16+1)
1/2P=(5^4-1)(5^4+1)(5^8+1)(5^16+1)
1/2P=(5^8-1)(5^8+1)(5^16+1)
1/2P=(5^16-1)(5^16+1)
1/2P=5^32-1
P=(5^32-1):1/2=2(5^32-1)
\(2P=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(2P=\left(5^{16}-1\right)\left(5^{16}+1\right)\Rightarrow2P=5^{32}-1\Rightarrow P=\frac{5^{32}-1}{2}\)
Đặt \(A=12.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(\Rightarrow2A=24.\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^2-1\right).\left(5^2+1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^4-1\right).\left(5^4+1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^8-1\right).\left(5^8+1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}-1\right).\left(5^{16}+1\right)\)
\(2A=\left(5^{16}\right)^2-1^2\)
\(2A=5^{32}-1\)
\(\Rightarrow A=\frac{5^{32}-1}{2}.\)